Sensors 2014, 14, 4126-4143; doi:10.3390/s140304126 OPEN ACCESS sensors ISSN 1424-8220 www.mdpi.com/journal/sensors Article Contour-Based Corner Detection and Classification by Using Mean Projection Transform Seyed Mostafa Mousavi Kahaki *, Md Jan Nordin and Amir Hossein Ashtari Center for Artificial Intelligence Technology, Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia (UKM), Bangi, Selangor 43600, Malaysia; E-Mails: [email protected] (M.J.N.); [email protected] (A.H.A.) * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +60-17-673-1264; Fax: +60-3-8925-6732. Received: 10 December 2013; in revised form: 3 February 2014 / Accepted: 12 February 2014 / Published: 28 February 2014 Abstract: Image corner detection is a fundamental task in computer vision. Many applications require reliable detectors to accurately detect corner points, commonly achieved by using image contour information. The curvature definition is sensitive to local variation and edge aliasing, and available smoothing methods are not sufficient to address these problems properly. Hence, we propose Mean Projection Transform (MPT) as a corner classifier and parabolic fit approximation to form a robust detector. The first step is to extract corner candidates using MPT based on the integral properties of the local contours in both the horizontal and vertical directions. Then, an approximation of the parabolic fit is calculated to localize the candidate corner points. The proposed method presents fewer false-positive (FP) and false-negative (FN) points compared with recent standard corner detection techniques, especially in comparison with curvature scale space (CSS) methods. Moreover, a new evaluation metric, called accuracy of repeatability (AR), is introduced. AR combines repeatability and the localization error ( ) for finding the probability of correct detection in the target image. The output results exhibit better repeatability, localization, and AR for the detected points compared with the criteria in original and transformed images. Keywords: corner detection; contour-based corner detector; mean projection transform; polygonal approximation Sensors 2014, 14 4127 1. Introduction Feature detection is a fundamental issue in image processing and computer vision that is directly related to interest points. Corner points are considered important features for feature extraction [1]. Corner detection is a low-level image processing technique that is widely used in different computer vision applications [2], such as camera calibration [3], target tracking [4], transformed image identification (TII) [5], image registration [6], 3D polyhedral building modelling from aerial imagery [7], multi-scale feature extraction from LIDAR data [8], 2D and 3D building extraction [9,10], and automotive applications [11]. However, different approaches require a different perspective for the corner definition. Historically, the terms of the corner point refer to the terms of both the interest point and the region of interest [12]. Generally, the corner detection in an image is the point on the contour at which two straight edges meet at a particular angle or the location at which the direction of the contour changes significantly [2]. Numerous corner detection methods have been introduced over the last several decades. These methods can be divided into three main categories: intensity-based detectors [13–17], model-based detectors [18,19], and contour-based detectors [1,4,20–25]. Each category has its own competencies for different types of areas and images. Recently, the third category has received more attention in terms of robustness and efficient computational cost. Model-based detectors extract the corner points by matching a predefined corner model to the image and calculating the similarity for detecting corner points. Their algorithms limit the detection to specific tasks, such as finding chessboard corners [3]. For general and flexible corner detection, defining a general corner model is difficult and does not cover all types of corners for different image types with different scene properties. Intensity-based detectors attract more attention than model-based detectors [1]. Intensity-based detectors use the grey-level information of the image to detect the corner points by applying the first- or second-order derivative on the images. The second-order derivatives of intensity-based methods are noise sensitive and are rarely used in the literature [1]. In 1977, Moravec [14] introduced the idea of finding the corner points as „points of interest‟ that have high-intensity variations in the vertical and horizontal directions. Harris and Stephen [15] proposed the most famous corner detector method, known as the Harris (Plessey) method, to improve upon Moravec‟s idea. The Harris method is based on approximates of the auto-correlation of the gradient in different directions. The Harris method is the most well-known method in the literature, but it cannot detect high-order corners [1]. A high-order corner is a point at which three or more contour regions meet [1]. The Harris method uses the Gaussian filter to reduce the FP corners in noisy images and increases the localization accuracy of the detector. Noble [26] proved that the Harris corner detector is only robust in „L‟-type corners. Based on these weaknesses, Shi and Tomasi [13] improved the Harris detector with a minor correction and calculated the minimum eigenvalues. Smith and Brady [16] introduced the Smallest Uni-value Segment with an Assimilating Nucleus (SUSAN), which used a gradient convolution of a circle mask called the USAN area to detect the corner points on a grey-level image. Yang et al. [27] improved the SUSAN method using a self-adoptive threshold and a rotating coordinate system, but the method was not sufficient for high accuracy of localization. Several improvements have been proposed for the Harris and SUSAN methods [28–36]. Grey-scale methods are sensitive to noise and are not as accurate for detecting the exact corner point location. Sensors 2014, 14 4128 Robustness to noise is an important issue for contour-based detectors [37], and researchers have proposed several algorithms over the last decade to address this problem. Contour-based detectors consist of three main steps: edge detection, contour extraction, and decision making on the contour [1]. The basic idea of contour-based methods was proposed by Rosenfeld and Johnston [23] in 1973 to calculate the angle of the curves on digital imagery. Subsequently, Kitchen and Rosenfeld [38] introduced their corner detector based on the change in direction of the gradient (first- and second-order derivatives) on the contour. This method is considered the first cornerness measure of the edge map in the literature. Coeurjolly et al. [39] extended the Worring and Smeulders [40] corner classification to a discrete method based on an estimation of the discrete osculating circle. Nguyen and Debled-Rennesson [41] extended the estimator proposed in [39] using blurred segments. Malgouyres et al. [42] introduced a discrete binomial convolution for a convergent estimator to reduce the noise effect. Kerautret and Lachaud [43] subsequently introduced a discrete curvature estimation-based method to calculate the curvature radius passing from the corner points. Over the last two decades, curvature scale space (CSS) methods have been widely used as corner detectors in the literature due to their high performance. CSS-based detectors exhibit some weaknesses, which are considered in this paper. They generally use second-order derivatives, which can cause an increase in the FP rate because of contour variation. Additionally, they require a Gaussian scale selection to smooth the curve area, which is application based and a difficult task. The basic idea was introduced by Rattarangsi and Chin [44] in 1992, and the basic CSS-based methods were proposed by Mokhtarian and Suomela [20] in 1998 and modified by Han and Poston [21] in 2001. CSS-based detectors use several planar curves that are smoothed using multi-scale Gaussian functions to calculate the local curvatures. Thresholding is used to remove the FP corner points from the candidate corners. CSS-based detectors are sensitive to noise on the contour, and the curvature estimation uses high-order derivatives to reduce the localization accuracy and high false rate [37]. A large-scale Gaussian function reduces noise but affects the corner localization, whereas a small-scale Gaussian function is sensitive to noise. To address these problems, Awrangjeb and Lu [37] proposed chord-to-point distance accumulation (CPDA) using the adoptive threshold method based on Han and Poston‟s idea [21]. The CPDA method uses a discrete curvature estimation that is more robust to the local variation. These authors used three chords of different lengths to estimate three normalized discrete curvature values at each point of the smoothed curve. They then multiplied the normalized values to achieve the curvature product. The candidate corners were selected from the maximum of the absolute curvature products. Because intensity variation information is not effective for extracting the corner candidate [1], a universal corner model (UCM) was proposed in [1] using the anisotropic directional derivative (ANDD) filter to improve the CPDA method to reduce the effect of the intensity variation of the contour and improve the localization accuracy. The proposed kernel in the ANDD filter is